Linear Operators: Spectral operators |
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Page 2144
... topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) A ( od ) . = It is seen , by using the above remarks , that for a fixed o the family of 8 for which the equation is valid is a o - field . Thus if o is in ...
... topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) A ( od ) . = It is seen , by using the above remarks , that for a fixed o the family of 8 for which the equation is valid is a o - field . Thus if o is in ...
Page 2203
... topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 4 , and since B generates ( B ) , the sets σ ( E ) form a subbasis for the ...
... topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 4 , and since B generates ( B ) , the sets σ ( E ) form a subbasis for the ...
Page 2256
... topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different from zero is contained in an arbitrarily small ...
... topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different from zero is contained in an arbitrarily small ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero